Question: $78$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $112$ less than $4$ times the number of away team fans. How many home team and away team fans attended the game?
Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 78}$ ${x = 4y-112}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${4y-112}$ for $x$ in the first equation. ${(4y-112)}{+ y = 78}$ Simplify and solve for $y$ $ 4y-112 + y = 78 $ $ 5y-112 = 78 $ $ 5y = 190 $ $ y = \dfrac{190}{5} $ ${y = 38}$ Now that you know ${y = 38}$ , plug it back into ${x = 4y-112}$ to find $x$ ${x = 4}{(38)}{ - 112}$ $x = 152 - 112$ ${x = 40}$ You can also plug ${y = 38}$ into ${x+y = 78}$ and get the same answer for $x$ ${x + }{(38)}{= 78}$ ${x = 40}$ There were $40$ home team fans and $38$ away team fans.